Random Dot Product Graph Models for Social Networks

2007 ◽  
pp. 138-149 ◽  
Author(s):  
Stephen J. Young ◽  
Edward R. Scheinerman
Keyword(s):  
Social Networks ◽  
Graph Models ◽  
Product Graph ◽  
Dot Product

The clustering methods in graph models of social networks

2017 ◽  
Vol 11 ◽  
pp. 1007-1017 ◽  
Author(s):  
Tatiana Victorovna Zudilova ◽  
Sergei Evgenievich Ivanov
Keyword(s):  
Social Networks ◽  
Clustering Methods ◽  
Graph Models

Measurement Error and Attenuation Bias in Exponential Random Graph Models

2016 ◽  
Vol 7 (1-2) ◽  
pp. 29-54
Author(s):  
Yeaji Kim ◽  
Leonardo Antenangeli ◽  
Justin Kirkland
Keyword(s):  
Social Networks ◽  
Random Graph ◽  
Measurement Errors ◽  
Asymptotic Properties ◽  
Exponential Random Graph Models ◽  
Graph Models ◽  
Random Graph Models ◽  
Exponential Random Graph ◽  
The Face ◽  
Distributed Measurement

AbstractExponential Random Graph Models (ERGMs) are becoming increasingly popular tools for estimating the properties of social networks across the social sciences. While the asymptotic properties of ERGMs are well understood, much less is known about how ERGMs perform in the face of violations of the assumptions that drive those asymptotic properties. Given that empirical social networks rarely meet the strenuous assumptions of the ERGM perfectly, practical researchers are often in the position of knowing their coefficients are imperfect, but not knowing precisely how wrong those coefficients may be. In this research, we examine one violation of the asymptotic assumptions of ERGMs – perfectly measured social networks. Using several Monte Carlo simulations, we demonstrate that even randomly distributed measurement errors in networks under study can cause considerable attenuation in coefficients from ERGMs, and do real harm to subsequent hypothesis tests.

scholarly journals What Graphs are 2-Dot Product Graphs?

2021 ◽  
pp. 1-16
Author(s):  
Matthew Johnson ◽  
Daniël Paulusma ◽  
Erik Jan van Leeuwen
Keyword(s):  
Social Networks ◽  
Product Formula ◽  
Np Hard ◽  
Intersection Graphs ◽  
Graph Classes ◽  
Product Graphs ◽  
Positive Threshold ◽  
Dot Product ◽  
Vector Formula ◽  
Dot Product Graphs

Let [Formula: see text] be an integer. From a set of [Formula: see text]-dimensional vectors, we obtain a [Formula: see text]-dot by letting each vector [Formula: see text] correspond to a vertex [Formula: see text] and by adding an edge between two vertices [Formula: see text] and [Formula: see text] if and only if their dot product [Formula: see text], for some fixed, positive threshold [Formula: see text]. Dot product graphs can be used to model social networks. Recognizing a [Formula: see text]-dot product graph is known to be NP -hard for all fixed [Formula: see text]. To understand the position of [Formula: see text]-dot product graphs in the landscape of graph classes, we consider the case [Formula: see text], and investigate how [Formula: see text]-dot product graphs relate to a number of other known graph classes including a number of well-known classes of intersection graphs.

scholarly journals The generalized centrality method for analyzing network cyberspace

2019 ◽  
pp. 55-64
Author(s):  
Natalia Nikolaevna Gorlushkina ◽  
Sergei Evgenievich Ivanov ◽  
Lubov Nikolaevna Ivanova
Keyword(s):  
Mathematical Model ◽  
Social Networks ◽  
Information Dissemination ◽  
Relative Weight ◽  
Graph Model ◽  
Graph Models ◽  
Number Of Factors ◽  
The Subject ◽  
Comparison Of The Results ◽  
Centrality Analysis

The subject of the research is the methods of network cyberspace analysis based on graph models. The analysis allows to find leaders of groups and communities, to find cohesive groups and visualize the results. The main methods of the graph theory used for cyberspace social networks are the methods of analyzing the centrality to determine the relative weight or importance of the vertices of the graph. There are known methods for analyzing centralities: by degree, by proximity, by mediation, by radiality, by eccentricity, by status, eigenvector, referential ranking. The disadvantage of these methods is that they are based only on one or several properties of the network participant. Based on the centrality analysis methods, a new generalized centrality method is proposed, taking into account such participant properties as the participant's popularity, the importance and speed of information dissemination in the cyberspace network. A mathematical model of a new method of generalized centrality has been developed. Comparison of the results of the presented method with the methods of the analysis of centralities is performed. As a visual example, a subgroup of cyberspace consisting of twenty participants, represented by a graph model, is analyzed. Comparative analysis showed the accuracy of the method of generalized centrality, taking into account at once a number of factors and properties of the network participant.

scholarly journals Majority Vote in Social Networks: Make Random Friends or Be Stubborn to Overpower Elites

2021 ◽  
Author(s):  
Charlotte Out ◽  
Ahad N. Zehmakan
Keyword(s):  
Social Networks ◽  
Real World ◽  
Majority Vote ◽  
Graph Models ◽  
Stabilization Time ◽  
The Real ◽  
Random Graph Models ◽  
Small Set ◽  
High Degree ◽  
Majority Model

Consider a graph G, representing a social network. Assume that initially each node is colored either black or white, which corresponds to a positive or negative opinion regarding a consumer product or a technological innovation. In the majority model, in each round all nodes simultaneously update their color to the most frequent color among their connections. Experiments on the graph data from the real world social networks (SNs) suggest that if all nodes in an extremely small set of high-degree nodes, often referred to as the elites, agree on a color, that color becomes the dominant color at the end of the process. We propose two countermeasures that can be adopted by individual nodes relatively easily and guarantee that the elites will not have this disproportionate power to engineer the dominant output color. The first countermeasure essentially requires each node to make some new connections at random while the second one demands the nodes to be more reluctant towards changing their color (opinion). We verify their effectiveness and correctness both theoretically and experimentally. We also investigate the majority model and a variant of it when the initial coloring is random on the real world SNs and several random graph models. In particular, our results on the Erdős-Rényi, and regular random graphs confirm or support several theoretical findings or conjectures by the prior work regarding the threshold behavior of the process. Finally, we provide theoretical and experimental evidence for the existence of a poly-logarithmic bound on the expected stabilization time of the majority model.

scholarly journals Generalized Random Dot Product graph

2019 ◽  
Vol 148 ◽  
pp. 143-149
Author(s):  
Tin Lok James Ng ◽  
Thomas Brendan Murphy
Keyword(s):  
Product Graph ◽  
Dot Product
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